Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
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he classical Kepler problem, as well as its quantum mechanical version,
the hydrogen atom, enjoys a well-known hidden symmetry, the conservation
of the Laplace-Runge-Lenz vector, which makes these problems
superintegrable. Is there a relativistic quantum field theory extension
that preserves this symmetry? In this Letter we show that the answer is
positive: in the nonrelativistic limit, we identify the dual conformal
symmetry of planar N=4
super Yang-Mills theory with the well-known symmetries of the hydrogen
atom. We point out that the dual conformal symmetry offers a novel way
to compute the spectrum of bound states of massive W
bosons in the theory. We perform nontrivial tests of this setup at weak
and strong coupling and comment on the possible extension to arbitrary
values of the coupling.
Original language | English |
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Article number | 161601 |
Journal | Physical Review Letters |
Volume | 113 |
Issue number | 16 |
ISSN | 0031-9007 |
DOIs | |
Publication status | Published - 16 Oct 2014 |
ID: 139036438